People often say mathematicians are not afraid of anything—except one thing: the Collatz Conjecture.
It is one of the most famous unsolved mysteries in mathematics.
Here’s how it works:
Pick any positive number.
If the number is odd, multiply it by 3 and add 1.
If the number is even, divide it by 2.
Now repeat this process again and again.
For example, start with 7:
7 is odd → 3×7 + 1 = 22
22 is even → 22 ÷ 2 = 11
11 is odd → 3×11 + 1 = 34
…and so on we get:
7 → 22 → 11 → 34 → 17 → 52 → 26 → 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
The surprising claim is this: no matter which number you start with, you will always eventually reach 1.
It sounds simple, but no one has been able to prove that it is true for all numbers. That’s why it remains a mystery.
Here's a cool math fact: If we can go up a set of stairs at one or two steps at a time, the number of different ways we can go up those stairs will always be a Fibonacci number! Here's why:
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